The wave equation for the ideal (lossless, linear, flexible)
vibrating string, depicted in Fig.C.1, is given by

(C.1)

where

where ``
'' means ``is defined as.'' The wave equation is
derived in §B.6. It can be interpreted as a statement
of Newton's second law, ``force = mass
acceleration,''
on a microscopic scale. Since we are concerned with transversevibrations on the string, the relevant restoring force (per unit
length) is given by the string tension times the curvature of the
string (
); the restoring force is balanced at all times by the
inertial force per unit length of the string which is equal to mass
density times transverse acceleration (
).